Dielectron and heavy-quark production in inelastic and high-multiplicity proton-proton collisions at $\sqrt{s}$ = 13 TeV

The measurement of dielectron production is presented as a function of invariant mass and transverse momentum ($p_{\rm T}$) at midrapidity ($|y_{\rm e}|<0.8$) in proton-proton (pp) collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV. The contributions from light-hadron decays are calculated from their measured cross sections in pp collisions at $\sqrt{s}=7$ TeV or 13 TeV. The remaining continuum stems from correlated semileptonic decays of heavy-flavour hadrons. Fitting the data with templates from two different MC event generators, PYTHIA and POWHEG, the charm and beauty cross sections at midrapidity are extracted for the first time at this collision energy: ${\rm d}\sigma_{\rm c\bar{c}}/{\rm d}y|_{y=0}=974\pm138(\rm{stat.})\pm140(\rm{syst.})~\mu{\rm b}$ and ${\rm d}\sigma_{\rm b\bar{b}}/{\rm d}y|_{y=0}=79\pm14(\rm{stat.})\pm11(\rm{syst.})~\mu{\rm b}$ using PYTHIA simulations and ${\rm d}\sigma_{\rm c\bar{c}}/{\rm d}y|_{y=0}=1417\pm184(\rm{stat.})\pm204(\rm{syst.})~\mu{\rm b}$ and ${\rm d}\sigma_{\rm b\bar{b}}/{\rm d}y|_{y=0}=48\pm14(\rm{stat.})\pm7(\rm{syst.})~\mu{\rm b}$ for POWHEG. These values, whose uncertainties are fully correlated between the two generators, are consistent with extrapolations from lower energies. The different results obtained with POWHEG and PYTHIA imply different kinematic correlations of the heavy-quark pairs in these two generators. Furthermore, comparisons of dielectron spectra in inelastic events and in events collected with a trigger on high charged-particle multiplicities are presented in various $p_{\rm T}$ intervals. The differences are consistent with the already measured scaling of light-hadron and open-charm production at high charged-particle multiplicity as a function of $p_{\rm T}$. Upper limits for the contribution of virtual direct photons are extracted at 90% confidence level and found to be in agreement with pQCD calculations.


Introduction
Heavy-flavour quarks (charm and beauty) are copiously produced by inelastic partonic scatterings in high-energy proton-proton (pp) collisions at the CERN Large Hadron Collider (LHC). Their large masses (m Q ) make it possible to calculate their production cross sections with perturbative quantum chromodynamics (pQCD) [1-3]. Hence, experimental measurements of heavy-quark production provide an excellent test of pQCD in this energy regime. Flavour conservation allows heavy quarks to be only produced in pairs. Charm hadrons and their decay products reflect the initial angular correlation of the heavy-quark pairs, whereas in the case of decays of beauty hadrons the correlation is weakened due to their large masses. The contribution from the simultaneous semileptonic decays of the corresponding heavy-flavour hadron pairs dominates the dilepton yield in the intermediate mass region (IMR) 1 < m < 3 GeV/c 2 . Hence, dielectron measurements can be used to study charm and beauty production.
The ALICE Collaboration has reported charm and beauty production cross sections measurements at midrapidity (|y| < 0.5) in pp collisions at centre-of-mass energies of √ s = 2.76 and 7 TeV [4-10]. The charm measurement at √ s = 7 TeV is complemented by ATLAS data extending to higher transverse momentum (p T ) and |y| < 2.1 [11]. Furthermore, the CMS Collaboration has provided a variety of charm and bottom measurements at midrapidity at √ s = 2.76, 5 and 7 TeV [12][13][14][15][16][17][18][19][20]. At forward rapidity (2 < y < 5), the LHCb Collaboration has measured charm and beauty production cross sections in pp collisions at √ s = 5, 7, 8 and 13 TeV [21][22][23][24]. These results are generally in good agreement with pQCD calculations at next-to-leading order (NLO) in the strong coupling constant (α s ) with all-order resummation of the logarithms of p T /m Q (FONLL) [1][2][3]. Though the measured charm production cross sections consistently lie on the upper edge of the systematic uncertainties of the theory calculations. Recently, the ALICE Collaboration has measured the charm and beauty production cross sections in pp collisions at √ s = 7 TeV using electron-positron pairs (dielectrons) from correlated semileptonic decays of heavy-flavour hadrons [25]. Such an approach was first performed by the PHENIX Collaboration in pp and d-Au collisions at √ s NN = 200 GeV at the Relativistic Heavy Ion Collider (RHIC) [26][27][28]. These measurements have the advantage that they probe the full p T range of heavy-quark pairs and contain complementary information about the initial correlation of charm quarks, i. e. the underlying production mechanism, which is not accessible in conventional single heavy-flavour measurements.
The measurement of direct photons, i. e. those produced in hard scatterings between incoming partons in hadronic collisions, provides another important test of pQCD. Furthermore, at p T < 3 GeV/c, where the applicability of perturbation theory may be questionable, experimental data of direct-photon production in pp collisions serve as a crucial reference to establish the presence of thermal radiation from the hot and dense medium created in heavy-ion collisions [29][30][31][32]. The measurement of real (massless) direct photons at low p T is challenging because of the large background of hadron decay photons. This background can be largely reduced by measuring the contribution of virtual direct photons, i. e. direct e + e − pairs, to the dielectron invariant-mass spectrum above the π 0 mass [29, 30].
Proton-proton collisions in which a large number of charged particles are produced have recently attracted the interest of the heavy-ion community [33,34]. These events exhibit features that are similar to those observed in heavy-ion collisions, e. g. collective effects, such as long-range angular correlations [35][36][37][38][39][40] or enhanced strangeness production [41]. Charged-hadron p T spectra in pp collisions at √ s = 13 TeV show a hardening with increasing multiplicity, an effect that arises naturally from jets [42]. Also, heavy-quark production is found to scale faster than linearly with the charged-particle multiplicity in pp collisions at √ s = 7 TeV [43,44]. This motivates the study of dielectron production in highmultiplicity pp collisions. In the low mass region (m ee < 1 GeV/c 2 ), dielectron measurements provide further insight into possible modifications of the light vector and pseudo-scalar meson production via their resonance and/or Dalitz decays, whereas in the IMR they allow for complementary studies of the heavy-flavour production. At LHC energies, the contribution from open charm already dominates the dielectron continuum at m ee ≈ 0.5 GeV/c 2 . Moreover, if a thermalised system were created in such The data samples used in this letter were recorded with ALICE in 2016 during the LHC pp run at √ s = 13 TeV. For the minimum-bias event trigger that is used to define the data sample for the analysis of inelastic pp collisions, coincident signals in both V0 scintillators are required to be synchronous with the beam crossing time defined by the LHC clock. Events with high charged-particle multiplicities are triggered on by additionally requiring the total signal amplitude measured in the V0 detector to exceed a certain threshold. At the analysis level, the 0.036 percentile of inelastic events with the highest V0 multiplicity (V0M) is selected to define the high-multiplicity event class. This value is low enough to avoid inefficiencies due to trigger threshold variations during data taking. Track segments reconstructed in the SPD are extrapolated back to the beam line to define the interaction vertex. Events with multiple vertices identified with the SPD are tagged as pile-up and removed from the analysis [48]. The vertex information may be improved based on the information provided by tracks reconstructed in the ITS and TPC. To assure a uniform detector coverage within |η| < 0.8, the vertex position along the beam direction is restricted to ±10 cm around the nominal interaction point. A total of 455×10 6 minimum-bias (MB) pp events and 79.2 × 10 6 high-multiplicity pp events are considered for further analysis, which corresponds to an integrated luminosity of L MB int = 7.87 ± 0.40 nb −1 and L HM int = 2.79 ± 0.15 pb −1 , respectively. The luminosity determination is based on the visible cross section for the V0-based minimum-bias trigger, measured in a van der Meer scan carried out in 2015 [50]. A conservative uncertainty of 5% is assigned to this measurement, to account for possible variations of the cross section between the two data-taking Dielectron production in pp collisions at √ s = 13 TeV ALICE Collaboration periods.

Data analysis
Electron 1 candidates are selected from charged-particle tracks reconstructed in the ITS and TPC in the kinematic range |η e | < 0.8 and p T, e > 0.2 GeV/c. Basic track quality criteria are applied, e. g. a sufficient number of space points measured in the TPC and ITS as well as a good track fit. The contribution from secondary tracks is reduced by requiring a maximum distance of closest approach (DCA) to the primary vertex in the transverse plane (DCA xy < 1.0 cm) and in the longitudinal direction (DCA z < 3.0 cm). To further suppress the contribution from photon conversions in the detector material, electron candidates are required to have a hit in the first SPD layer and no ITS clusters shared with other reconstructed tracks.
The electron identification is based on the complementary information provided by the TPC and TOF. The detector PID response, n(σ DET i ), is expressed in terms of the deviation between the measured and expected value of the specific ionisation energy loss in the TPC or time-of-flight in the TOF for a given particle hypothesis i and momentum, normalised by the detector resolution (σ DET ). In the TPC, electrons are selected in the range n σ TPC e < 3 and pions are rejected by requiring n σ TPC π > 4. Furthermore, kaons and protons are rejected with n σ TPC K > 4 and n σ TPC p > 4, unless the candidate is positively identified as an electron in the TOF, i. e. fulfilling n σ TOF e < 3. For particles that are outside n σ TPC K < 4 and n σ TPC p < 4 the TOF information is only used to select electron candidates with n σ TOF e < 3 if the track has an associated hit in the TOF detector.
Since experimentally the origin of each electron or positron is unknown, all electron candidates are paired considering combinations with opposite (N +− ) but also same-sign charge (N ±± ). Most of the electron pairs arise from the combination of two electrons originating from different mother particles. These pairs give rise to the combinatorial background B that is estimated via the geometric mean of samesign pairs √ N ++ N −− within the same event. Such pairs include correlated background, e. g. originating from π 0 decays with two e + e − pairs in the final state (π 0 → γ ( * ) γ ( * ) → e + e − e + e − ), which includes decay channels with real photons and their subsequent conversion in detector material. Such processes lead to opposite and same-sign pairs at equal rate. The background estimate needs to be corrected for the different detector acceptance of opposite and same-sign pairs. This correction factor is determined by dividing the yields of uncorrelated opposite (M +− ) and same-sign pairs (M ±± ) in mixed events: The signal S is shown together with the opposite-sign spectrum N +− and the combinatorial background B in Fig. 1 for minimum-bias and high-multiplicity events. In the mass interval 0.2 < m ee < 3 GeV/c 2 , the signal-to-background ratio varies in MB events between 0.3 and 0.04 with a minimum around m ee ≈ 0.5 GeV/c 2 and is roughly constant at 0.2 in the IMR [51]. In HM events, the minimum reaches 0.01 and is about 0.08 in the IMR.
Electron-positron pairs from photon conversion in the detector material, contributing to the low mass spectrum below 0.14 GeV/c 2 , are removed by using their distinct orientation relative to the magnetic field [25]. m ee and pair transverse momentum p T, ee separately for the different e + e − sources: resonance and Dalitz decays of relevant mesons as well as correlated semileptonic decays of charm and beauty hadrons. The total signal reconstruction efficiency is obtained by weighting the efficiency of each dielectron source by its expected contribution and is found to be about 20% in 0.7 < m ee < 1.2 GeV/c 2 and approaches 30% at lower and higher masses.
Different aspects of the analysis are considered as possible sources of systematic uncertainties, which are summarised in Table 1. The systematic uncertainties due to the track reconstruction are estimated by comparing the efficiency of the ITS-TPC matching, the requirement of a hit in the first SPD layer, and the requirement of no shared ITS clusters in MC simulations and data. The residual disagreements between data and MC add to a 6.5% uncertainty on the single track level, which leads to a 13% uncertainty for pairs. The MC simulations were also checked to reproduce all details of the PID selection within a systematic uncertainty of 2% for e + e − pairs. The purity of the electron sample is estimated to be >93% over the relevant p T range, with a p T -integrated hadron contamination of about 4%. The resulting hadron contamination on the dielectron signal is found to be negligible. For m ee < 0.14 GeV/c 2 , a 2% uncertainty on the conversion rejection was estimated from the yield change when tightening the selection to reject photon conversions. A 2% uncertainty on the signal yield due to the correction factor R is obtained by repeating the event mixing in different event classes, defined by the position of the reconstructed primary vertex and by the charged-particle multiplicity. The efficiency of the minimumbias trigger to select inelastic events with an e + e − pair in the ALICE acceptance (|η e | < 0.8 and p T, e > 0.2 GeV/c) is estimated to be (99 ± 1)% from the Monash 2013 tune of PYTHIA 8. This and the luminosity uncertainty of 5% [50] are global uncertainties, which are not included in the point-to-point uncertainties. No significant variation of systematic uncertainties on mass or p T, ee is observed in the analysis, and the same total uncertainty of 14% is assigned as point-to-point correlated uncertainties on the differential dielectron cross section in inelastic pp collisions.
The analysis of the high-multiplicity data has additional systematic uncertainties. First, no dedicated high-multiplicity MC simulation was performed. In such events the vertex distribution is biased more than in MB events by the asymmetric pseudorapidity coverage of the two V0 detectors. The change of the detector acceptance with vertex position could lead to a difference in the number of reconstructed electrons of up to 3%, which results in an uncertainty of 6% for e + e − pairs. Second, a possible multiplicity dependence of the reconstruction and PID efficiency is covered by an uncertainty of 6% [57]. Added in quadrature, this amounts to a total uncertainty of 15%.

Cocktail of known hadronic sources
The dielectron spectrum measured in pp collisions at √ s = 13 TeV is compared with the expectations from all known hadron sources, i. e. the hadronic cocktail, contributing to the dielectron spectrum in the ALICE central barrel acceptance (|η e | < 0.8 and p T, e > 0.2 GeV/c). A fast MC simulation is used to estimate the contribution from π 0 , η, η , ρ, ω and φ decays in pp collisions, as detailed in [25].
Following the approach outlined in [58], the pion p T -spectrum at √ s = 13 TeV is approximated by scaling the p T -spectrum of charged hadrons [42] by the pion-to-hadron ratio measured at √ s = 7 TeV [59, 60]. The difference with respect to the same procedure based on the pion-to-hadron ratio measured at √ s = 2.76 TeV [59, 61] is smaller than 1% at low p T and reaches 5% at high p T . The charged hadron p T -spectra at √ s = 13 TeV are normalised to INEL>0 events rather than INEL events. This is corrected taking the 21% difference in the p T integrated dN ch /dη values for these two event classes [42]. A conservative uncertainty of 10% is assigned on this extrapolation.
A fit of the obtained charged-pion p T -spectrum with a modified Hagedorn function is then taken as proxy for the neutral-pion p T -distribution. The simulated cross section per unit rapidity of the π 0 is dσ /dy| y=0 = 155.2 mb. For the η meson a fit of the measured η/π 0 ratio in pp collisions at √ s = 7 TeV is used [62]. The Monash 2013 tune of PYTHIA 8 describes the ρ/π 0 and ω/π 0 ratios measured in pp collisions at √ s = 2.76 and 7 TeV, respectively [55, 56]. Therefore, MC simulations obtained with this tune at √ s = 13 TeV are used to obtain the ρ/π 0 and ω/π 0 ratios. Based on the η/π 0 , ρ/π 0 and ω/π 0 data, the ratios at high p T are 0.5 ± 0.1, 1.0 ± 0.2 and 0.85 ± 0.17, respectively. The η and φ mesons are generated assuming m T scaling, replacing p T with m 2 − m 2 π + (p T /c) 2 [63]. For the m T scaling, particle yields are normalised at high p T relative to the π 0 yield: 0.40 ± 0.08 for η (from PYTHIA 6 calculations) and 0.13 ± 0.04 for φ [64]. The detector response, including momentum and angular resolutions, as well as Bremsstrahlung effects obtained from full MC simulations, is applied to the decay electrons as a function of p T, e , η e and the azimuth ϕ e . The following sources of systematic uncertainties were evaluated: the input parameterisations of the measured spectra as a function of p T (π ± , η/π 0 and ω/π 0 ), the branching fractions of all included decay modes, the m T scaling parameters and the resolution smearing. For the high-multiplicity cocktail, the input hadron p T -distributions are adjusted according to the measured modifications of the charged-hadron p T spectra [42]. The uncertainties of the cocktail from light-hadron decays are about ±15%, reaching up to +50% in the region dominated by the η meson due to uncertainties in the extrapolation to low p T . The multiplicity dependence has an uncertainty that varies between about 12% at low p T and 40% at high p T .
The Perugia 2011 tune of PYTHIA 6.4, which includes NLO parton showering processes, is used to estimate the contributions of correlated semileptonic decays of open charm and beauty hadrons [53, 65]. As an alternative, the NLO event generator POWHEG is also considered [66-69]. The resulting same-sign spectrum is subtracted from the opposite-sign distribution as in the data analysis. Detector effects are implemented as for the light-hadron cocktail. The spectra are normalised to cross sections at midrapidity −16 µb at √ s = 13 TeV. The quoted uncertainties take into account both the measured uncertainty and the FONLL extrapolation uncertainties. The latter (dominated by scale uncertainties but also including PDF and mass uncertainties) are considered to be fully correlated between the two energies [71]. For the high-multiplicity cocktail, the open charm contribution is weighted as a function of p T according to the measured enhancement of D mesons with p T > 1 GeV/c at √ s = 7 TeV [43]. The same weights are applied to the open beauty contribution as no significant difference between the production of D mesons and J/ψ from beauty-hadron decays is observed [43]. For electrons originating from charm or beauty hadrons with p T < 1 GeV/c, the same weight as for 1 < p T < 2 GeV/c is assumed in the absence of a measurement. This leads to an uncertainty on the multiplicity dependence of about 40% at low p T decreasing to 20% at high p T .
The J/ψ contribution is simulated with PYTHIA 6.4 and normalised to the cross section at √ s = 13 TeV, extrapolated with FONLL [9] from the measurement at √ s = 7 TeV by the ALICE Collaboration [72]. In the high-multiplicity cocktail, the J/ψ is scaled according to a dedicated, p T -integrated measurement [44].

Results
The dielectron cross sections are reported within the ALICE central barrel acceptance |η e | < 0.8 and p T, e > 0.2 GeV/c, i. e. without correction to full phase space. The result, integrated over p T, ee < 6 GeV/c, is shown as a function of m ee in the left panel of Fig. 2. The data are compared with the expectation from the hadronic decay cocktail, using PYTHIA for the heavy-flavour components, and found to be in agreement within uncertainties. Good agreement between data and cocktail calculations is also found as a function of p T, ee , which is shown for three m ee intervals in the right panel of Fig. 2.   Figures 3 and 4 show the ratios of the dielectron spectra in high-multiplicity over inelastic events as a function of m ee for different p T, ee intervals. To account for the trivial scaling with charged-particle multiplicity, the ratio is scaled by the factor dN ch /dη(HM)/ dN ch /dη(INEL) = 6.27 ± 0.22, where dN ch /dη(HM) = 33.29 ± 0.39 and dN ch /dη(INEL) = 5.31 ± 0.18 are the charged-particle multiplic-Dielectron production in pp collisions at √ s = 13 TeV ALICE Collaboration ities in |η ch | < 0.5 measured in high-multiplicity and inelastic pp collisions, respectively [42]. In this ratio, the multiplicity-independent uncertainties cancel and the total systematic uncertainty reduces to 9%. The ratio is in good agreement with the hadronic decay cocktail calculations over the whole measured m ee and p T, ee range. In particular for π 0 and η mesons, this confirms the hypothesis that the different light mesons have the same multiplicity dependence as a function of m T , which was used in the construction of the high-multiplicity hadron cocktail. From the agreement between data and cocktail in the high-p T range (3 < p T, ee < 6 GeV/c 2 ), which is dominated by open beauty, it can be also concluded that the open beauty production has a multiplicity dependence similar to that of open charm.  Table 2. The first uncertainty is the statistical uncertainty resulting from the fits and the second is the systematic uncertainty, which is determined by moving the data points coherently upward and downward by their systematic uncertainties and repeating the fits. The branching fraction of charm-hadron decays to electrons is taken as (9.6 ± 0.4 ± 1.1)% [73]. This translates into a 24% uncertainty at the pair level. Alternatively, a comparable uncertainty is obtained when considering the measured charm-hadron abundances [8] and their branching fractions of semileptonic decays [74]. In this case, the uncertainty arises from different Λ c /D 0 ratios measured by the ALICE Collaboration, 0.500 ± 0.061 (stat.) ± 0.160 (syst) (for p T > 1 GeV/c) in pp collisions at √ s = 7 TeV [75], and, e. g. the LEP average of 0.113 ± 0.013 ± 0.006 [76]. The branching fraction of beauty hadrons decaying into electrons, including via intermediate charm hadrons, is (21.53 ± 0.63)% [74], which leads to a 6% uncertainty on the dielectron-based cross section measurement. Like the statistical and systematic uncertainties, these branching fraction uncertainties are fully correlated between the PYTHIA and POWHEG based results.
The results are consistent with extrapolations from lower energies based on pQCD calculations discussed in the previous section. There is a strong anti-correlation between the fitted charm and beauty cross sections. The sizeable difference in the cross sections between the two MC event generators are comparable to what is observed at √ s = 7 TeV [25]. The different cross sections obtained from fits with PYTHIA and POWHEG simulations are caused by acceptance differences of e + e − pairs from heavy-flavour hadron decays in these two event generators because of different kinematic correlations of the heavy quark pairs, in particular in rapidity. This points to important differences in the heavy quark production mechanisms Dielectron production in pp collisions at √ s = 13 TeV ALICE Collaboration between the two generators. It should be stressed that single heavy-flavour measurements appear insensitive to these differences as the cross sections obtained from such measurements agree between PYTHIA and POWHEG based extrapolations [7, 11, 22]. Therefore, dielectrons provide complementary information on heavy-flavour production that, if properly modelled, should lead to consistent cross sections with PYTHIA and POWHEG. Table 2 also summarises the corresponding cross sections for the high-multiplicity data. In case of PYTHIA, the measured charm cross section translates into an enhancement of 1.86±0.40 (stat.)±0.40 (syst.) relative to the charged-particle multiplicity increase. This is consistent with the modelled multiplicity dependence used as input for the cocktail in Figs. 3 and 4. For the beauty cross section the observed enhancement is 1.63 ± 0.50 (stat.) ± 0.35 (syst.). This is consistent with the multiplicity dependence observed for open charm, but a scaling with charged-particle multiplicity cannot be excluded.
The fraction of real direct photons to inclusive photons can be extracted from the dielectron spectrum at small invariant masses assuming the equivalence between this fraction and the ratio of virtual direct photons to inclusive photons. The data are fitted, in bins of p T, ee , with the sum of the light-flavour cocktail ( f LF (m ee )), open heavy-flavour contribution ( f HF (m ee )) and a virtual direct photon component ( f direct (m ee )), whose shape is described by the Kroll-Wada equation [77,78]  1/m ee dependence. The direct-photon fraction r is then extracted by fitting the data in the mass interval 0.14 < m ee < 0.32 GeV/c 2 , i. e. above the π 0 mass to suppress the most dominant hadron background, with the following expression: dσ /dm ee = r f dir (m ee ) + (1 − r) f LF (m ee ) + f HF (m ee ).
No significant direct photon contribution is observed in neither the inelastic nor the high-multiplicity events [51]. Upper limits at 90% confidence level (C.L.) are extracted with the Feldman-Cousins method [79] and summarised in Table 3 together with predictions from perturbative QCD calculations for inelastic events [80]. The current uncertainties prevent any conclusions on the scaling of direct-photon production with charged-particle multiplicity.

Summary and conclusion
We have presented the first measurement of dielectron production at midrapidity (|y e | < 0.8) in protonproton collisions at √ s = 13 TeV. The dielectron continuum can be well described by the expected contributions from decays of light-and heavy-flavour hadrons. The charm and beauty cross sections are extracted for the first time at midrapidity at √ s = 13 TeV and are consistent with extrapolations from lower energies based on pQCD calculations. The differences observed between POWHEG and PYTHIA imply different kinematic correlations of the heavy-quark pairs in these two event generators. Therefore dielectrons are uniquely sensitive to the heavy quark production mechanisms. The comparison of the dielectron spectra in inelastic events and in events with high charged-particle multiplicities does not reveal modifications of the spectrum beyond the already   hadrons. The upper limits on the direct-photon fractions are consistent with predictions from perturbative quantum chromodynamics calculations.

Acknowledgements
The ALICE Collaboration would like to thank Werner Vogelsang for providing the NLO pQCD calculations for direct photon production.